Self-similar solutions of NLS-type dynamical systems
solv-int
2007-05-23 v1 Exactly Solvable and Integrable Systems
Abstract
We study self-similar solutions of NLS-type dynamical systems. Lagrangian approach is used to show that they can be reduced to three canonical forms, which are related by Miura transformations. The fourth Painleve equation (PIV) is central in our consideration - it connects Heisenberg model, Volterra model and Toda model to each other. The connection between the rational solutions of PIV and Coulomb gas in a parabolic potential is established. We discuss also the possibility to obtain an exact solution for optical soliton i.e. of the NLS equation with time-dependent dispersion.
Keywords
Cite
@article{arxiv.solv-int/9909021,
title = {Self-similar solutions of NLS-type dynamical systems},
author = {M. Boiti and V. G. Marikhin and F. Pempinelli and A. B. Shabat},
journal= {arXiv preprint arXiv:solv-int/9909021},
year = {2007}
}
Comments
18 pages, AmsTeX